Defect diagnosis method and defect diagnosis apparatus

ABSTRACT

A method for diagnosis of a defect of an object to be inspected, such as a rotational machine, etc., by measuring a vibration generated thereby, wherein a measured signal generated by the object is detected, an amplitude probability density function of wave-form of the obtained measured signal is expanded orthogonally through a Gram-Charlier series, and the Gram-Charlier series are calculated so as to make diagnosis of defect(s) in the object to be inspected.

BACKGROUND OF THE INVENTION Field of the Invention

The present invention relates to a defect diagnosis in a frictionsystem, such as bearings and/or gears in a rotational machine, and to adefect diagnosis in a construction system, such as an unbalance inrotating masses and/or a misalignment where two rotational machines runoff an axis thereof.

A sudden and/or unexpected stoppage of manufacturing machinery equipmentbrings about extremely large economic loss. In facilities utilizing themanufacturing equipment, precautionary maintenance is practiced forpreventing such trouble such as a sudden unexpected stoppage. As anexample of the method of precautionary maintenance for preventing suchtrouble, a sound or/and a vibration being generated by the machineryequipment in operation is measured so as to determine the conditionthereof. Such a procedure is called a “state-base precaution”. Here, theconventional arts will be explained in terms of the state-baseprecaution, by taking a vibration measurement as an example.

When making the diagnosis of the presence of troubles by measuring thevibration of machinery equipment, it is decided whether the measuredvibration exceeds a reference value or not in the magnitude thereof.Ordinarily, two kinds of reference values are prepared for thedecisions. Namely, if the detected value exceeds the reference valuebeing the smaller of the reference values, it is found to be in a domainof caution, therefore observation must be performed frequently, thoughthe equipment operation will be continued. If the detected value exceedsthe reference value being the larger of the reference values, it isfound to be in a domain of danger, therefore equipment operation must bestopped in order for the equipment to be restored or repairedimmediately. When the state of the machinery equipment reaches to thecaution domain, a time when it reaches to the danger domain is predictedfrom a guide such as a chart or a graph indicating a tendency in thepast of changes from a normal state into the caution domain, so as toprovide for production planning which has the highest economicefficiency and a planning of maintenance, including the restoration orrepair.

The equipment of the manufacturing machines located in a factory orworks of a company varies depending upon the purposes thereof, i.e.,there are used various kinds or sorts of machinery, being different inrevolution speed, electric power consumption (torque), and/or loads,including large or small values thereof, or a machine having a largevibration or one having a small vibration.

Each reference value for deciding the presence of the defect or failureis unique and characteristic to each particular machinery equipment, andthe reference values are decided on the basis of a large accumulatednumber of sample data representative of the defect or failureconditions, as well as those representative of the normal conditions.However, for fully obtaining the effect of the state-base precaution, anappropriate reference value for decision is needed.

A significant investment of labor is needed to determine the abovereference for decision, since enough sample data may not be obtainabledue to a rareness or scarcity of the troubles or accident, or since thekinds or sorts of the machines to be inspected is too large in number.Further, there are many companies which cannot apply the state-basemaintenance, because of such reasons as that there is no engineer formaintenance work who has applied knowledge in trouble or defectdiagnosis, therefore the sample data cannot be gathered.

Though the state-base maintenance is an economical and superior methodof maintenance with reduced costs or expenses, the most suitablepossible decision reference or criterion must be decided upon so as toapply the state-base maintenance, as mentioned previously. Manycompanies are unable to apply the state-base maintenance, since thisreference for decision cannot be appropriately decided thereby.

SUMMARY OF THE INVENTION

According to the present invention, an object is to provide a diagnosismethod wherein attention is paid to a difference of a probabilitydensity function of amplitude obtained by normalizing a wave-form of ameasured signal, such as the wave-form of vibration which is generatedby the machine, from a normal distribution, thereby proposing thedecision criterion which can be applied in common to the differentfacilities of many rotational machines, and also to provide a trouble ordefect diagnosis apparatus comprising those functions.

The present invention is based upon a principle that the amplitudeprobability density function of a measured signal, such as the vibrationbeing generated by an object to be detected, for example, a machine,etc., operating under a normal condition, coincides with the normaldistribution, however, it is shifted from the normal distribution whentrouble or abnormal condition arises in the machine.

According to the present invention, while no component informationrelating to the measured signal is utilized, such as the amplitude andthe vibration number thereof which is generated by the object such as amachine to be inspected, the normalized amplitude probability densityfunction is decided to coincide with the normal distribution or not,fully independent of specifications such as the revolution number, theelectric power consumption, the load and the scale of the structure ofthe machine.

Namely, according to the present invention, there is provided a defectdiagnosis method for an object to be inspected, comprising:

detecting a measured signal being generated by said object to beinspected;

expanding orthogonally an amplitude probability density function of awave-form of the obtained measured signal in a Gram-Charlier series; and

calculating the Gram-Charlier series so as to make a diagnosis of adefect in the object to be inspected.

Here, the defect in the present invention means indicates the conditionwhere the machine operates differently from operation under the normalcondition, but not that it is already in an inoperable condition.

Further, according to the present invention, there is provided a defectdiagnosis method for an object to be inspected, comprising:

detecting a measured signal being generated by said object to beinspected;

expanding orthogonally an amplitude probability density function of awave-form of the obtained measured signal in a Gram-Charlier series; and

Further, according to the present invention, there is provided a defectdiagnosis method for an object to be inspected, comprising:

detecting a measured signal being generated by said object to beinspected;

expanding a wave-form of the obtained measured signal obtained in aFourier series to obtain a frequency spectrum;

expanding orthogonally an amplitude probability density function byviewing the obtained frequency spectrum from an axis of an amplitudethereof in a Gram-Charlier series; and

calculating the Gram-Charlier series so as to make diagnosis of a defectin said object to be inspected.

Further, according to the present invention, there is provided a defectdiagnosis method for an object to be inspected, comprising:

detecting a measured signal being generated by said object to beinspected;

expanding a wave-form of the obtained measured signal in a Fourierseries to obtain a frequency spectrum;

expanding orthogonally an amplitude probability density function byviewing the obtained frequency spectrum from an axis of an amplitudethereof in a Gram-Charlier series; and

calculating a difference from a normal distribution so as to make adiagnosis of a defect in the object to be inspected. In the inventiondefined in the above, the measured signal may be a vibration.

In the invention defined in the above, the measured signal may be anacoustic, an acoustic emission, fluctuations of current or of effectiveelectric power rather than a vibration.

In the invention defined in the above, the object to be inspected caninclude a vehicle, an aircraft and a construction other than an ordinarymachine.

Furthermore, according to the present invention, there is provided adefect diagnosis apparatus for implementing the defect diagnosis method,comprising a probe with respect to the object to be inspected.

Here, a method with use of an expanding equation of the Gram-Charlierseries will be explained in detail below.

The amplitude probability density function of the normal distributionN(μ,σ²) can be expressed as follows, assuming that an averaged value isμ and a dispersion is σ².${f(x)} = {\frac{1}{\sigma \sqrt{2\pi}}^{- \frac{{({x - \mu})}^{2}}{2\sigma^{2}}}}$

Here, by making the averaged value μ=0 and the dispersion σ²=1, thenormalized N(0,1) can be expressed as follows:${f(x)} = {\frac{1}{\sqrt{2\pi}}^{- \frac{x^{2}}{2}}}$

where, φ(x) is as follows. ${\phi (x)} = ^{- \frac{x^{2}}{2}}$

It is presumed that an arbitrary density function p(x) can be expandedin the following form with use of a normal distribution density functionφ(x) and a derived function thereof: $\begin{matrix}{{p(x)} = {{c_{0}{\phi^{(0)}(x)}} + {\frac{c_{1}}{1!}{\phi^{(1)}(x)}} + {\frac{c_{2}}{2!}{\phi^{(2)}(x)}} + {\frac{c_{3}}{3!}{\phi^{(3)}(x)}} + {\frac{c_{4}}{4!}{\phi^{(4)}(x)}} + \ldots}} & (1)\end{matrix}$

where the φ^((n))(x) is expressed by a polynomial of Hermite as below.

φ^((n))(x)=(−1)^(n) H _(n)(x)φ(x)  (2)

And the equation (1) is derived as follows. $\begin{matrix}{{p(x)} = {{c_{0}{H_{0}(x)}{\phi (x)}} - {\frac{c_{1}}{1!}{H_{1}(x)}{\phi (x)}} + {\frac{c_{2}}{2!}{H_{2}(x)}{\phi (x)}} - {\frac{c_{3}}{3!}{H_{3}(x)}{\phi (x)}} + {\frac{c_{4}}{4!}{H_{4}(x)}{\phi (x)}} - \ldots + {\frac{c_{n}}{n!}{H_{n}(x)}{\phi (x)}} - \ldots}} & (3)\end{matrix}$

Then, by differentiating the normal distribution density function φ(x),the following φ^((n))(x) is obtained:

φ⁽¹⁾(χ)=−xe ^(−x) ² ² =−x·φ(x)

φ⁽²⁾(x)=−φ(x)−x·φ⁽¹⁾(x)=−φ(x)+x ²·φ(x)=(x ²−1)·φ(x)

 φ⁽³⁾(x)=2x·φ(x)+(x ²−1)·φ⁽¹⁾(x)=2x·φ(x)−(x ²−1)·x·φ(x)=−(x ³−3x)·φ(x)

φ⁽⁴⁾(x)=(−3x ²+3)·φ(x)−(x ³−3x)·φ⁽¹⁾(x)=(−3x ²+3)·φ(x)+(x³−3x)·x·φ(x)=(x ⁴−6x ²+3)·φ(x)

φ⁽⁵⁾(x)=(4x ³−12x)·φ(x)+(x ⁴−6x ²+3)·φ⁽¹⁾(x)=(4x ³−12x)·φ(x)−(x ⁴−6x²+3)·x·φ(x)=−(x ⁵−10x ³+15x)·φ(x)

φ⁽⁶⁾(x)=(−5x ⁴+30x ²−15)·φ(x)−

(x ⁵−10x ³+15x)·φ⁽¹⁾(x)=

(−5x ⁴+30x ²−15)·φ(x)+

(x ⁵−10x ³15x)·x·φ(x)=

(x ⁶−15x ⁴+45x ²−15)·φ(x)

From those differentiating values and the above equation (2), thefollowing can be obtained:

H ₀(x)=1

H ₁(x)=x

H ₂(x)=x ²−1

H ₃(x)=x ³−3x

H ₄(x)=x ⁴−6x ²+3

H ₅(x)=x ⁵−10x ³+15x

H ₆(x)=x ⁶−15x ⁴+45x ²−15

Further, the polynomial of Hermite has an orthogonality as below:$\begin{matrix}{{\int_{- \infty}^{\infty}{{H_{m}(x)}{H_{n}(x)}{\phi (x)}}} = {{\delta_{mn}(x)} = \quad {{m!}\quad \left( {m = n} \right)}}} \\{= \quad {0\quad \left( {m \neq n} \right)}}\end{matrix}$

An integration is executed by multiplying H_(n)(x) at the both sides ofthe equation (3):${\int_{- \infty}^{\infty}{{H_{n}(x)}{p(x)}{x}}} = {{c_{0}{\int_{- \infty}^{\infty}{{H_{n}(x)}{H_{0}(x)}{\phi (x)}}}} - {\frac{c_{1}}{1!}{\int_{- \infty}^{\infty}{{H_{n}(x)}{H_{1}(x)}{\phi (x)}}}} + {\frac{c_{2}}{2!}{\int_{- \infty}^{\infty}{{H_{n}(x)}{H_{2}(x)}{\phi (x)}}}} - {\frac{c_{3}}{3!}{\int_{- \infty}^{\infty}{{H_{n}(x)}{H_{3}(x)}{\phi (x)}}}} + {\frac{c_{4}}{4!}{\int_{- \infty}^{\infty}{{H_{n}(x)}{H_{4}(x)}{\phi (x)}}}} - \ldots + {\frac{c_{n}}{n!}{\int_{- \infty}^{\infty}{{H_{n}(x)}{H_{n}(x)}{\phi (x)}}}} - \ldots}$

Since the Hermite polynomial has the orthogonality, only the clauseshaving the same order, and derived is the following: $\begin{matrix}{{{\left( {- 1} \right)^{n}{\int_{- \infty}^{\infty}{{H_{n}(x)}{p(x)}{x}}}} = c_{n}}\begin{matrix}{c_{0} = \quad {\int_{- \infty}^{\infty}{{p(x)}{x}}}} \\{c_{1} = \quad {- {\int_{- \infty}^{\infty}{{x \cdot {p(x)}}{x}}}}} \\{c_{2} = \quad {{\int_{- \infty}^{\infty}{\left( {x^{2} - 1} \right){p(x)}{x}}} = {{\int_{- \infty}^{\infty}{x^{2}{p(x)}{x}}} - {\int_{- \infty}^{\infty}{{p(x)}{x}}}}}} \\{c_{3} = \quad {{- {\int_{- \infty}^{\infty}{\left( {x^{3} - {3x}} \right){p(x)}{x}}}} = {{- {\int_{- \infty}^{\infty}{x^{3}{p(x)}{x}}}} + {3{\int_{- \infty}^{\infty}{{x \cdot {p(x)}}{x}}}}}}} \\{{c_{4} = \quad {{\int_{- \infty}^{\infty}{\left( {x^{4} - {6x^{2}} + 3} \right){p(x)}{x}}} = {{\int_{- \infty}^{\infty}{x^{4}{p(x)}{x}}} - {6{\int_{- \infty}^{\infty}{x^{2}{p(x)}{x}}}} +}}}\quad} \\{\quad {3{\int_{- \infty}^{\infty}{{p(x)}{x}}}}} \\{c_{5} = \quad {{- {\int_{- \infty}^{\infty}{\left( {x^{5} - {10x^{3}} + {15x}} \right){p(x)}{x}}}} = {{- {\int_{- \infty}^{\infty}{x^{5}{p(x)}{x}}}} +}}} \\{\quad {{10{\int_{- \infty}^{\infty}{x^{3}{p(x)}{x}}}} - {15{\int_{- \infty}^{\infty}{{x \cdot {p(x)}}{x}}}}}} \\{c_{6} = \quad {\int_{- \infty}^{\infty}{\left( {x^{6} - {15x^{4}} + {45x^{2}} - 15} \right){p(x)}{x}}}} \\{= \quad {{\int_{- \infty}^{\infty}{x^{6}{p(x)}{x}}} - {15{\int_{- \infty}^{\infty}{x^{4}{p(x)}{x}}}} + {45{\int_{- \infty}^{\infty}{x^{2}{p(x)}{x}}}} -}} \\{\quad {15{\int_{- \infty}^{\infty}{{p(x)}{x}}}}}\end{matrix}} & (4)\end{matrix}$

Here, it is assumed that n number of time series data λ_(i) arecollected from the vibration data which the machine generates.

Then, the average value μ is obtained as follows, and the total data isshifted by the average value (λ_(i)=λ_(i)−μ).$\mu = \frac{\sum\limits_{i = 1}^{n}\lambda_{i}}{n}$

Next, an effective value σ is obtained as is expressed below, so as tonormalize the total data (λ_(i)=λ_(i)/σ).$\sigma = \sqrt{\frac{\sum\limits_{i = 1}^{n}\lambda_{i}^{2}}{n}}$

The following summations are obtained from the time series data whichare normalized:${s_{0} = n},\quad {s_{1} = {\sum\limits_{i = 1}^{n}\lambda_{i}}},\quad {s_{2} = {\sum\limits_{i = 1}^{n}\lambda_{i}^{2}}},\quad {s_{3} = {\sum\limits_{i = 1}^{n}\lambda_{i}^{3}}},{s_{4} = {\sum\limits_{i = 1}^{n}\lambda_{i}^{4}}},\quad {s_{5} = {\sum\limits_{i = 1}^{n}\lambda_{i}^{5}}},\quad {s_{6} = {\sum\limits_{i = 1}^{n}\lambda_{i}^{6}}},\ldots$

Then, those summations are divided by the number of the data as follows:${s_{0} = {{n/n} = 1}},\quad {s_{1} = {\frac{\sum\limits_{i = 1}^{n}\lambda_{i}}{n} = 0}},\quad {s_{2} = {\frac{\sum\limits_{i = 1}^{n}\lambda_{i}^{2}}{n} = 1}},\quad {s_{3} = \frac{\sum\limits_{i = 1}^{n}\lambda_{i}^{3}}{n}}$${s_{4} = \frac{\sum\limits_{i = 1}^{n}\lambda_{i}^{4}}{n}},\quad {s_{5} = \frac{\sum\limits_{i = 1}^{n}\lambda_{i}^{5}}{n}},\quad {s_{6} = \frac{\sum\limits_{i = 1}^{n}\lambda_{i}^{6}}{n}},\ldots$

By inserting them into those coefficient c_(j), then the following isobtained:

c ₀ =s ₀=1

c ₁ =−s ₁=0

c ₂ =s ₂ −s ₀=0

c ₃ =−s ₃+3s ₁ =−s ₃

c ₄ =s ₄−6s ₂+3s ₀ =s ₄−3

c ₅ =−s ₅+10s ₃−15s ₁ =−s ₅+10s ₃

c ₆ =s ₆−15s ₄+45s ₂−15s ₀ =s ₆−15s ₄+30

By the normalization as in the above, c₀=1 and c₁=c₂=0, therefore acompensated clause starts with the third clause.

The coefficient c_(j) can be expressed as below.

c ₃ =−s ₃

c ₄ =s ₄−3

c ₅ =−s ₅+10s ₃

c ₆ =s ₆−15s ₄+30

The series being obtained by the expansion in this manner is called theGram-Charlier series. The Gram-Charlier series contain therein elementsof the defect or trouble and deterioration. However, mathematically, asthe Gram-Charlier series are in orthogonal relationships with eachother, the elements of the defects and deterioration contained thereincan be considered to be totally independent of each other.

When the amplitude probability density function is the normaldistribution, all of the Gram-Charlier series become zero. When thecondition comes into the defect or trouble and shifts from the normaldistribution, each absolute value of these numeral (series) valuesbecomes large. Accordingly, by determining the criterion or referencevalue of the Gram-Charlier series, it is possible to make diagnosis ofthe defects or troubles.

From the equation (3), the arbitrary density function p(x) becomes asfollows: $\begin{matrix}{{p(x)} = {\left( {1 + {\frac{c_{3}}{3!}\left( {x^{3} - {3x}} \right)} + {\frac{c_{4}}{4!}\left( {x^{4} - {6x^{2}} + 3} \right)} + {\frac{c_{5}}{5!}\left( {x^{5} - {10x^{3}} + {15x}} \right)} + {\frac{c_{6}}{6!}\left( {x^{6} - {15x^{4}} + {45x^{2}} - 15} \right)} + \ldots}\quad \right\} {\phi (x)}}} & (5)\end{matrix}$

This is called a Gram-Charlier distribution function. This Gram-Charlierdistribution function is the function which is the most analogous orapproximated to the amplitude probability density function which isactually measured.

The arbitrary density function can be expressed by a sum of the normaldistribution density function φ(x) and a differentiation function r(x),as shown in the following equation:

p(x)=φ(x)+r(x)

where the difference function r(x) becomes as below from the equation(5): $\begin{matrix}{{r(x)} = {{{p(x)} - {\phi (x)}} = {\left( {{\frac{c_{3}}{3!}\left( {x^{3} - {3x}} \right)} + {\frac{c_{4}}{4!}\left( {x^{4} - {6x^{2}} + 3} \right)} + {\frac{c_{5}}{5!}\left( {x^{5} - {10x^{3}} + {15x}} \right)} + {\frac{c_{6}}{6!}\left( {x^{6} - {15x^{4}} + {45x^{2}} - 15} \right)} + \ldots}\quad \right){\phi (x)}}}} & (6)\end{matrix}$

Then, the next equation is defined: $\begin{matrix}{\delta = {\int_{- 6}^{6}{\left( {r(x)} \right)^{2}{x}}}} & (7)\end{matrix}$

where a square integration value of the difference function r(x) from 6to −6 is the difference δ.

The difference δ is zero when the amplitude probability density functionis coincident with the normal distribution, while the numeral valuecomes to be large when being in the condition of the defect or troubleand shifted from the normal distribution. Accordingly, by determiningthe criterion or the reference value of the difference δ, it is possibleto make the diagnosis of the defect or trouble.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 shows an example of normal data for explaining a principle in theoperation of the present invention, in particular, the wave-form of avibration acceleration generated from a bearing under a normalcondition;

FIG. 2 shows a curve of tracking of a Gram-Charlier distributionfunction which is obtained upon the basis of the vibration accelerationwave-form data generated from the bearing under the normal condition anda normal distribution for comparison;

FIG. 3 shows an example of abnormal or defect data for explaining theprinciple in the operation of the present invention, in particular, thewave-form of a vibration acceleration generated from a bearing having adefect or trouble therein;

FIG. 4 shows a tracking curve of the difference function which isobtained upon the basis of the vibration acceleration wave-form datagenerated from a bearing that can be decided to be defected or broken;

FIG. 5 shows the construction of a defect diagnosis apparatus accordingto the present invention; and

FIG. 6 shows a block diagram of the defect diagnosis apparatus accordingto the present invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Hereinafter, detailed explanation of the embodiments according to thepresent invention will be given by referring to attached drawings.

FIG. 1 shows a wave-form of a vibration acceleration under the normalcondition of a bearing. The Gram-Charlier series of this wave-form areobtained.

Obtaining the summation value of s₃-s₆ after being shifted by a directcurrent component of the wave-form and normalized with effective values,the s₃-s₆ are as follow;

s ₃=−0.02568, s ₄=2.9750, s ₅=−0.74344 and s ₆=15.065

and the obtained Gram-Charlier series of this wave-form are thefollowing:

c ₃=0.02568, c ₄=−0.02497, c ₅=1.0002 and c ₆=0.43950

The reference values or criteria for decision are determined as L=4 andH=10 from a large number of data which are stored or accumulated, and amethod for decision is as follows:${{(1)\quad {normal}\quad {when}\quad \frac{c_{3}^{2}}{3!}} < L},{{{and}\quad \frac{c_{4}^{2}}{4!}} < L},{{{and}\quad \frac{c_{5}^{2}}{5!}} < L},{{{and}\quad \frac{c_{6}^{2}}{6!}} < {{L(2)}\quad {danger}\quad {when}\quad \frac{c_{3}^{2}}{3!}} > H},{{{or}\quad \frac{c_{4}^{2}}{4!}} > H},{{{or}\quad \frac{c_{5}^{2}}{5!}} > H},{{{or}\quad \frac{c_{6}^{2}}{6!}} > H}$

(3) caution when it is not any one of them.

From the Gram-Charlier series obtained here, operation is decided to benormal.

Putting the obtained Gram-Charlier series up to the sixth (6^(th)) orderinto the equation (5), the Gram-Charlier distribution function isobtained and a track following it is shown in FIG. 2. A curve of abroken line in FIG. 2 shows the Gram-Charlier distribution function,while a solid shows the normal distribution. The difference δ calculatedfrom the equation (7) has an extremely small value, such as 0.003,therefore it is possible to determine that operation is normal.

Next, it is tried or applied to a bearing having a defect therein, withuse of the vibration acceleration data thereof. FIG. 3 shows thewave-form of the vibration acceleration of the bearing having a defecttherein.

Obtaining the summation value of s₃-s₆ after being shifting by a directcurrent component of the wave-form and normalized with effective values,the s₃-s₆ are as follows;

s ₃=−0.77954, s ₄=20.609, s ₅=−68.010 and s ₆=911.94

and the obtained Gram-Charlier series of this wave-form are thefollowing:

c ₃=0.77954, c ₄=17.609, c ₅=75.806 and c ₆=632.80

Based on those Gram-Charlier series obtained with the method mentionedpreviously, the condition is decided to be dangerous.

The difference function r(x), which is obtained by putting only thethird (3^(rd)) and the fourth (4^(th)) of the Gram-Charlier series intothe equation (6), is as follows:${r(x)} = {\left( {{\frac{0.77954}{3!}\left( {x^{3} - {3x}} \right)} + {\frac{17.609}{4!}\left( {x^{4} + {6x^{2}} + 3} \right)}} \right){\phi (x)}}$

and then, this difference function follows the track as shown in FIG. 4.

Here, calculating it on the basis of the equation (7), the difference δis 6.32. If the reference value or criterion for decision is 2.5, thenit is decided to be in the danger region or domain.

Next, detailed descriptions will be given with reference to concreteexamples.

(1) A First Example: Diagnostic apparatus for defect of friction type:

This apparatus makes diagnosis of a defect or trouble relating tofriction, such as abnormality in bearings, abnormality in gears,abnormality on belts or leakage, etc.

The construction of a defect diagnostic apparatus is shown in FIG. 5. Avibration sensor thereof is of a pressure-electric type, and thevibration acceleration of 20 kHz to 50 kHz is measured thereby.

A microcomputer performs the following calculation processing andinput/output processing of data. The results of the diagnosis aredisplayed on a liquid crystal display (LCD) as “normal”, “caution” or“danger”.

(1) Sample data x_(i) at number 4096 is memorized every 250 μsec, and atthe same time the following summation is executed:$s_{1} = {\sum\limits_{i = 1}^{4096}x_{i}}$

(2) The average value μ is obtained, i.e., μ=s_(i)/4096, then x_(i) isshifted by the average value μ so as to delete the DC componenttherefrom.

x _(i) =x _(i−μ)

(3) The effective value σ is obtained as below:${s_{2} = {\sum\limits_{i = 1}^{4096}x_{i}^{2}}},$

the effective value: $\sigma = {\sqrt{\frac{s_{2}}{4096}} = x_{rms}}$

and the x_(i) is normalized as below. $x_{i} = \frac{x_{i}}{\sigma}$

(4) The summation values of s₃ through s₆ are obtained as follows:$s_{3} = {{\sum\limits_{i = 1}^{4096}{x_{i}^{3}\quad s_{4}}} = {{\sum\limits_{i = 1}^{4096}{\left( x_{i}^{2} \right)^{2}\quad s_{6}}} = {\sum\limits_{i = 1}^{4096}\left( x_{i}^{3} \right)^{2}}}}$

and then averaged as below:

S ₃ =s ₃ /n S ₄ =s ₄ /n S ₆ =s ₆ /n

Next, abnormal coefficients are obtained by an expansion equation ofGram-Charlier, as below:

c ₃ =S ₃

c ₄ =S ₄−3

c ₆ =S ₆−15S ₄+30

(6) The conditions for the diagnosis of defect or trouble is as below:${{a\text{)}\quad {normal}\text{:}\quad {when}\quad \frac{c_{3}^{2}}{3!}} < L},{{{and}\quad \frac{c_{4}^{2}}{4!}} < L},{{{and}\quad \frac{c_{6}^{2}}{6!}} < L}$${{\text{b}\text{)}\quad {danger}\text{:}\quad {when}\quad \frac{c_{3}^{2}}{3!}} > H},{{{or}\quad \frac{c_{4}^{2}}{4!}} > H},{{{or}\quad \frac{c_{6}^{2}}{6!}} > H}$

c) caution: when the condition a) or b) is not satisfied, and L=4 andH=10.

(2) A Second Example:

Diagnostic apparatus for defect of construction:

This makes a diagnosis of a defect or trouble in construction, such asunbalance, decentering or eccentricity, misalignment, axial bending,relaxation or looseness, cracks, rattling or clattering, etc.

The construction of an apparatus is the same as in the first example,and the vibration acceleration is measured within a frequency range from10 kHz to 200 kHz.

(1) Time series data Xi at number 512 are memorized every 2 msec.

(2) The Fourier transformation is treated on the time series data X_(n)with weighting by means of Hunning window, and 200 power spectra f_(i)are obtained.

(3) The average value μ is obtained with respect to 191 power spectra byevery 1 Hz from 10 Hz to 200 Hz, as below:${s_{1} = {\sum\limits_{i = 10}^{200}f_{i}}},$

the average value: μ=s₁/191

and then, the power spectra f_(i) are shifted by the average value μ asbelow: f_(i)′=f_(i)−μ

(4) Then, the effective value σ is obtained as follows:$s_{2} = {\sum\limits_{i = 10}^{200}\left( f_{i}^{\prime} \right)^{2}}$

the effective value: $\sigma = \sqrt{\frac{s_{2}}{191}}$

and the power spectra f′_(i) is normalized as below:$f_{i}^{''} = \frac{f_{i}^{\prime}}{\sigma}$

(5) Considering f_(i)″ is a wave-form, the summations of s₃ through s₆are obtained from the spectrum data of number 191 as follows:$s_{3} = {{\sum\limits_{i = 10}^{200}{f_{i}^{3}\quad s_{4}}} = {{\sum\limits_{i = 10}^{200}{\left( f_{i}^{2} \right)^{2}\quad s_{6}}} = {\sum\limits_{i = 10}^{200}\left( f_{i}^{3} \right)^{2}}}}$

and then they are averaged as below:

S ₃ =s ₃ /n S ₄ =s ₄ /n S ₆ =s ₆ /n

(6) Next, abnormal coefficients are obtained by an expansion equation ofGram-Charlier, as below:

c ₃ =S ₃

c ₄ =S ₄−3

c ₆ =S ₆−15S ₄+30

(6) The conditions for the diagnosis of defect or trouble is as below:${{a\text{)}\quad {normal}\text{:}\quad {when}\quad \frac{c_{3}^{2}}{3!}} < L},{{{and}\quad \frac{c_{4}^{2}}{4!}} < L},{{{and}\quad \frac{c_{6}^{2}}{6!}} < L}$${{\text{b}\text{)}\quad {danger}\text{:}\quad {when}\quad \frac{c_{3}^{2}}{3!}} > H},{{{or}\quad \frac{c_{4}^{2}}{4!}} > H},{{{or}\quad \frac{c_{6}^{2}}{6!}} > H}$

c) caution: when the condition a) or b) is not satisfied, and L=4 andH=10.

(3) Other Example:

In the first and the second examples mentioned above, explanation of thepresent invention is applied to defect diagnosis apparatus operating onthe basis of vibration measurement, however the present invention shouldnot be restricted only to them. It can also applied to defect diagnosisapparatus operating on the basis of the measured signal of an acoustic,an acoustic emission, a fluctuation of current, a fluctuation ofeffective electric power, etc.

As is fully mentioned in the above, according to the present invention,by measuring a measured signal, such as the vibration which is generatedby the object to be detected, including a machine, and by determiningonly one reference value or criterion for decision with respect to thevalue so that the normalized probability density function of amplitudeshifts from the normal distribution, it is possible to achieve thedefect diagnosis apparatus which can diagnose a defect or trouble of theobject to be detected, including a large variety of rotational machineswhich are different in the specifications thereof.

What is claimed is:
 1. A method for diagnosis of a defect of an objectto be inspected, comprising: detecting a measured signal being generatedby said object to be inspected; expanding orthogonally an amplitudeprobability density function of a wave-form of the obtained measuredsignal in a Gram-Charlier series; and calculating the Gram-Charlierseries so as to make diagnosis of the defect in the object to beinspected.
 2. A method for diagnosis of a defect as defined in claim 1,wherein said measured signal is a vibration.
 3. A method for diagnosisof a defect as defined in claim 1, wherein said measured signal is anacoustic, an acoustic emission, a fluctuation of current or afluctuation of effective electric power.
 4. A method for diagnosis of adefect as defined in claim 1, wherein said object to be inspected is anyone of a machine, a vehicle, an aircraft and a building.
 5. A defectdiagnosis apparatus for implementing the method for diagnosis as definedin claim 1, comprising a probe which is made to touch the object to beinspected.
 6. A method for diagnosis of a defect of an object to beinspected, comprising: detecting a measured signal being generated bysaid object to be inspected; expanding orthogonally an amplitudeprobability density function of a wave-form of the obtained measuredsignal in a Gram-Charlier series; and calculating a difference from anormal distribution so as to make diagnosis of the defect in the objectto be inspected.
 7. A method for diagnosis of a defect of an object tobe inspected, comprising: detecting a measured signal being generated bysaid object to be inspected; expanding a wave-form of the obtainedmeasured signal in a Fourier series to obtain a frequency spectrum;expanding orthogonally an amplitude probability density function byviewing the obtained frequency spectrum from an axis of an amplitudethereof in a Gram-Charlier series; and calculating the Gram-Charlierseries so as to make diagnosis of the defect in the object to beinspected.
 8. A method for diagnosis of a defect of an object to beinspected, comprising: detecting a measured signal being generated bysaid object to be inspected; expanding a wave-form of the obtainedmeasured signal in a Fourier series to obtain a frequency spectrum;expanding orthogonally an amplitude probability density function byviewing the obtained frequency spectrum from an axis of an amplitudethereof in a Gram-Charlier series; and calculating a difference from anormal distribution so as to make diagnosis of the defect in the objectto be inspected.